摘要: The light-like cusp anomalous dimension is a universal function in the analysis
of infrared divergences. In maximally (N = 4) supersymmetric Yang–
Mills theory (SYM) in the planar limit, it is known, in principle, to all loop
orders. The non-planar corrections are not known in any theory, with the
first appearing at the four-loop order. The simplest quantity which contains
this correction is the four-loop two-point form factor of the stress tensor multiplet.
This form factor was largely obtained in integrand form in a previous
work for N = 4 SYM, up to a free parameter. In this work, a reduction
of the appearing integrals obtained by solving integration-by-parts (IBP)
identities using a modified version of Reduze is reported. The form factor
is shown to be independent of the remaining parameter at integrand level
due to an intricate pattern of cancellations after IBP reduction. Moreover,
two of the integral topologies vanish after reduction. The appearing master
integrals are cross-checked using independent algebraic-geometry techniques
explored in the Mint package. The latter results provide the basis of master
integrals applicable to generic form factors, including those in Quantum
Chromodynamics. Discrepancies between explicitly solving the IBP relations
and the MINT approach are highlighted. Remaining bottlenecks to
completing the computation of the four-loop non-planar cusp anomalous
dimension in N = 4 SYM and beyond are identified.